Complex RLC circuit analysis

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john williamsXT

Joined Jul 14, 2009
10
The attached circuit was referred to in my earlier thread Complex RLC circuit.
At t=0,i=0,q=q2=0.
I have been working for days on solving the differential equations for i1(t) and i2(t).
My expression for i1(t) is as follows.
\[
i_1(t)=0.16\cos{100t}+0.11\sin{100t}+(7.06)10^{-7}C_1e^{-1190t}+e^{-0.5t}(C_2\cos{31.6t}+C_3\sin{31.6t})
\]
Now I can apply the initial condition at t=0,i=i1=i2=0 then
\[
i_1(0)=0=0.16+(7.06)10^{-7}C_1+C_2
\]
Also
\[
(\frac{di_1}{dt})=0
\]
At t=0.
Which gives.
\[
11-(8.4)10^{-4}C_1-0.5C_2+31.6C_3=0
\]
My problem at this stage is finding another initial condition to give me a third equation to find all 3 constants?
Firstly can anyone confirm my solution for i1 and then supply another initial condition.
FOR THE ORIGINAL DIFFERENTIAL EQUATIONS PLEASE REFER BACK TO MY ORIGINAL THREAD.
Cheers
John
 

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